An interactive approach to multicriteria sorting for quasiconcave value functions

Abstract

In this article, we develop an interactive algorithm to place alternatives in ordered preference classes for a decision maker (DM) with an increasing quasiconcave value function. Such value functions are quite general in that they include linear and concave value functions. Our aim is to elicit sorting information from the DM as few times as possible; our algorithm places other alternatives using previous responses from the DM utilizing properties of quasiconcave value functions. As an application, we sort 81 global MBA programs into preference classes using criteria such as alumni career progress, idea generation, and diversity. We study the performance of our proposed algorithm, when we change the number of criteria, number of alternatives, and introduce response errors. © 2014 Wiley Periodicals, Inc. Naval Research Logistics 61: 447–457, 2014

Using convex preference cones in multiple criteria decision making and related fields

“…Moreover, they used their approach in a real-world application with the purpose of admitting students to Middle East Technical University, Turkey. The previous idea has been generalized to any number of classes in Ulu and Köksalan (2014). They refer to the problem as sorting.…”

Approaches for inequity-averse sorting

“…Other utility function forms such as linear [13], quasiconcave [14], and Tchebycheff [15] are also considered.…”

“…Constraint set (13) assigns values to the alternatives based on the assumption on the form of the utility function. Constraint sets (14) and (15) ensure that we have nondecreasing concave marginal utility functions. Constraint sets (16) and (17) are used for normalization purposes.…”

Interactive and nonparametric modeling of preferences on an ordinal scale using small data

“…In another study, Ulu and Köksalan (2014) Criteria Hierarchy Process (MHCP) framework proposed by Corrente et al (2012) to sorting problems. MHCP is developed to deal with multiple criteria in a hierarchical scheme, hence, large sets of criteria are partitioned into levels.…”

“…As clearly seen from Table 3, there are only three studies (Greco et al, 2002;Angilella et al, 2009;Ulu & Köksalan, 2014) Ulu and Köksalan 2014No In general, the main objective of the aforementioned techniques is to sort limited number of alternatives of the problem under consideration with maximum accuracy. They take a subset of the alternatives for getting preference information.…”